Optimal Planning of Electric Vehicle Charging Stations with DSTATCOM and PV Supports Using Metaheuristic Optimization

Abstract

This study investigates the optimal operation of distribution systems incorporating Photovoltaic (PV) units, Electric Vehicle Charging Stations (EVCSs), and DSTATCOM devices using the Starfish Optimization Algorithm (SFOA). The main goal of the SFOA is to minimize a combined function that encompasses three key objectives: reducing system losses, increasing PV capacity, and enhancing EVCS power. By applying the SFOA within a multi-objective optimization framework, the optimal locations and sizes of PV units, EVCSs, and DSTATCOMs are identified to meet these objectives. This study analyzes and compares several case studies with different numbers of EVCSs, focusing on the operation of a modified 51-bus distribution system over 24 h. Results show that PV hosting energy increases to 21.73, 23.83, and 29.22 MWh for cases with 1, 2, and 3 EVCSs, respectively. EVCS energy also rises to 12.41, 19.50, and 37.23 MWh for the same cases. The corresponding optimized DSTATCOM reactive powers are 11.02, 12.02, and 13.74 MVarh. Throughout all cases, system constraints—such as voltage limits, utility current, and power flow equations—remain within acceptable ranges. The findings demonstrate the SFOA’s effectiveness in optimizing distribution systems with various devices, ensuring efficient operation and meeting all key objectives while adhering to system constraints.

1. Introduction

Due to the widespread integration of Distributed Generation (DG) resources, such as renewable energy sources, into radial distribution systems (RDSs), distribution system operators (DNOs) must enhance reliability, functional costs, and power quality [1]. DNOs address this issue with the use of fixed or switched capacitors, network reconfiguration, and load management. Power flows in one direction; therefore, most distribution networks are radial or lightly meshed for convenience. Network reconfiguration, shunt capacitors, and DSTATCOM allocation are less expensive than the investment and procurement costs of DGs [2,3]. Shunt capacitors and Distribution Static Synchronous Compensator (DSTATCOM) devices introduce reactive power into the distribution network [4], whereas reconfiguration reconfigures the RDS topology and structure into a more efficient radial pattern. Shunt capacitors inject reactive power in predetermined steps, without accounting for the dynamic evolution of the RDS loads. A DSTATCOM, a power electronic device, can regulate reactive power injection or absorption based on the distribution network’s load demand. The RDS faces challenges with DGs, Electric Vehicles (EVs), and reactive compensation devices. These devices have been studied in various works in the literature.

Recently, a research study [5] proposed an innovative multi-timescale approach for managing photovoltaic (PV) charging stations with integrated Energy Storage Systems (ESS). The method reduced operational expenses by initially creating an appropriate day-ahead schedule for the battery system informed by predictions. It subsequently refined the timetable in real time using fresh data on solar generation and charging requirements. The findings indicated that the strategy effectively reduced forecast errors, substantially decreased daily operational costs, and ensured the reliable satisfaction of EV charging requirements. Another study [6] presented two EV charging techniques for office parking lots designed to mitigate the effects of EV charging on local power networks. The uncoordinated EV charging (UEVC) strategy functions autonomously, whereas the coordinated EV charging (CEVC) method aligns EV charging with solar photovoltaic generation and battery storage. The CEVC plan incorporated solar panels and batteries, synchronizing EV charging with renewable energy production to alleviate grid pressure and improve overall system efficiency. The authors of [7] examined the optimal design and techno-economic feasibility of on-grid PV systems for Omani households with EVCSs, taking into account local electricity rates for power purchase and sale to the utility grid. HOMER Grid software is used to simulate and optimize the system setup and EV charging schedule to minimize Net Present Cost (NPC) while meeting system limits. The capturing power from PV under certain conditions and general renewable energy sources were discussed in [8,9,10,11].

Optimization has been featured in various publications addressing the integration of EVCSs [12] with renewables into distribution systems. The study [13] advocated the use of the artificial bee colony (ABC) algorithm as an efficient tool for optimal energy management in hybrid microgrid systems that incorporate PV, wind turbines, fuel cells, microturbines, and BESS. The algorithm’s efficacy has been assessed under various levels of solar irradiance across four distinct operational scenarios. The study in [14] presented a two-stage optimization methodology for DS to safely and cost-effectively integrate EVCSs and DERs. In the first stage, suitable power demands and locations for different EVCSs are determined to ensure grid stability. Second, PV and WT are combined to minimize grid purchase costs and account for shifting electricity prices, thereby optimizing economic benefits. The Model optimized EVCS and DER placements and operations while maintaining voltage stability using a unique single-weight tree structure and the modified JAYA algorithm. A recent study [15] adopted the application of a fire hawk optimization (FHO) and a hybridized whale particle swarm optimization (HWPSO) to enhance the power quality of the distribution system by mitigating the adverse effects of EV loads, including power losses, voltage fluctuations, and voltage imbalance factors. The variability in solar power generation and the state of charge of electric vehicles is modeled using a Monte Carlo simulation. The study in [16], employed diverse algorithms to assess their efficacy in achieving the ideal distribution of various PV systems and WTs, while accounting for uncertainties in their electrical energy production and fluctuations in load demand throughout seasonal variations throughout the year. The convergence attributes and outcomes demonstrated that the marine predator algorithm (MPA) was the most rapid and efficient method for achieving optimal solutions after a limited number of iterations, in comparison to the other algorithms. Another study [17] employed a multi-objective PSO algorithm to optimize the placement of EVCSs, considering the surrounding region and station coverage. The MPSO algorithm optimizes the objective function to minimize the costs of charging site placement.

The integration of PV with EVCSs has been applied in various settings. The authors [18] optimized the placement of EV docking stations (EVDS) to satisfy charging needs efficiently, taking into consideration trip distances and energy consumption. The study used solar-powered stations in the IEEE 69 Bus distribution network to charge EVs, improving sustainability, reliability, and efficiency while reducing grid dependence. The authors [19] proposed an innovative mathematical modeling approach that incorporates various proportions of the impacts of EV charging on distribution networks, such as the proportion of customers on time-of-use (TOU) tariffs, EV penetration levels, various daily charging frequencies, and charging power levels. In a separate study [20], the authors examined the integration of solar PV generation with EVCS to reduce grid pressure and accelerate charging. The analysis identified the optimal sites and capacities for solar-augmented EVCSs to enhance efficiency and grid stability. They conducted sensitivity analyses of EV numbers and solar PV adoption across different EV charging rates. The study revealed how these variables affect network performance and the benefits of combining solar energy with EV charging infrastructure.

On the other hand, studies on microgrids or distribution systems integrated with reactive compensation have appeared in some publications. In a recent study [21], a DSTATCOM was proposed to improve power quality in a conventional bus system. A real-time dataset was obtained under various power quality disruptions. This dataset was used to train a deep learning controller to create the DSTATCOM pulse signal from bus voltages. Another study [22] proposed a strategic design of solar-renewable energy-integrated DSTATCOM-based charging stations for electric vehicles, using a ZIP load model, aligned with the Sustainable Development Goals, and addressing techno-economic and environmental concerns. The efficacy of the proposed work is demonstrated through the application of the PSO and TLBO algorithms to enhance system performance. A MATLAB-(Version 2022) developed Firefly algorithm optimized reactive power adjustment in an EVCS-equipped distribution system [23]. Different cases update the proposed approach for detecting the involvement of reactive power compensating units with EVCSs on a line-by-line basis. Reactive power compensation issues are addressed in the study to reduce energy losses and stabilize the power supply. In another study [24], the authors adopted the population-based genetic algorithm (PGA) to minimize operational costs, energy losses, and CO₂ emissions in microgrids incorporating wind turbines across various optimization scenarios. The proposed coordinated control technique for DGs offers flexibility to accommodate economic, technical, and environmental considerations while accounting for fluctuations in power generation and demand. A mixed-integer linear programming (MILP) model [25] was adopted to optimize the placement, sizing, and operation of PV units and DSTATCOMs in radial DSs. Multi-period optimization allowed PV units and DSTATCOMs to dispatch active and reactive power based on hourly load profiles. The CPLEX solver solved the AMPL-formulated optimization problem for global optimality and computing efficiency. A different research [26] developed a novel DSTATCOM allocation mechanism to reduce power losses, voltage variations, and capital expenditures in the power DSs using a modified Capuchin search algorithm (mCapSA). Additionally, the analytic hierarchy process was proposed to determine optimal objective function weights.

This study explores the optimal operation of distribution systems that include PV units, EVCSs, and DSTATCOM devices. A recent metaheuristic optimization method called the Starfish Optimization Algorithm (SFOA) is employed. The goal of SFOA is to minimize a combined function with three main objectives. It is applied in multi-objective optimization to reduce system losses, increase PV capacity, and enhance the power of the EVCS. The SFOA finds the best locations and sizes for PV units, EVs at stations, and DSTATCOM reactive power to achieve these goals. Several case studies with one, two, and three EVCSs are analyzed and compared. In this research, three locations for the DSTATCOM and PV units within the modified 51-bus distribution system are considered to optimize their operation over a 24 h period. Therefore, the main contributions of this work can be summarized as follows:

• Novel application of the Starfish Optimization Algorithm (SFOA) to distribution systems, simultaneously coordinating photovoltaic (PV) units, electric vehicle charging stations (EVCSs), and DSTATCOM devices within a unified multi-objective optimization framework.
• Integrated optimization strategy that reduces system losses, enhances PV hosting capacity, and improves EVCS power delivery, demonstrating the versatility of SFOA in addressing conflicting operational goals.
• Innovative siting and sizing methodology for PV units, EVCSs, and DSTATCOM reactive power support, enabling optimal deployment and operation under realistic distribution system constraints.
• Extensive case study validation, analyzing different EVCS penetration levels over 24 h operational horizons, and providing new insights into system stability and efficiency under dynamic load and generation conditions.
• The SFOA outperforms different optimization algorithms, including FPA, HHO, MVO, SMA, SSA, and PSO.

The rest of the paper is organized as follows. Section 2 provides a detailed modeling analysis of the distribution system and different sources, including the PV, DSC, and EVCSs. Section 3 presents the problem formulation, including the objective function calculations, the problem constraints, and the detailed formulation of the SFOA. Section 4 presents the simulation results and discussion, and Section 5 presents the main conclusions of the work.

2. System Modeling

The addition of Electric Vehicle Charging Stations (EVCSs) to the radial distribution system (RDS) has a significant impact on the overall grid infrastructure and energy landscape. Integrating EVCSs results in a noticeable increase in electricity demand in specific areas, such as parking lots and residential neighborhoods. This integration presents challenges for grid operators, as sudden spikes in electricity demand during peak charging times can overload the distribution system if not properly managed. The primary challenges for the Distribution System Operator (DSO) are maintaining stable voltage levels, minimizing losses, and ensuring overall system stability. On the other hand, incorporating EVCSs can promote the use of renewable energy sources by enabling innovative charging strategies that leverage solar or wind energy. To study the EDSs, the main components should be correctly modeled as demonstrated in the following sections.

2.1. Modeling of Distribution Systems

When the distribution systems are balanced, the analysis is provided per phase, with all phases identical except that the voltages and currents are shifted by 120 degrees. Moreover, distribution systems are renowned for not having mutual impedances or shunt capacitors, unlike transmission systems. In this case, the distribution system is modeled as a series impedance of the cable connecting two buses, with shunt demands at each bus. A single section of a distribution system consisting of only two buses, m, n, is shown in Figure 1. It is assumed that the PV units and DSTATCOM (DSC) devices are connected to the receiving end bus, n, as shown. At any bus, the load flow equations are satisfied, i.e., power is balanced at every bus of the system. Due to the existence of the line (branch) impedance, there are losses in it, and they are calculated as follows.

$${\mathrm{P}}_{\mathrm{l},\mathrm{m}\mathrm{n}}=\mathfrak{R}({\mathrm{I}}_{\mathrm{m}\mathrm{n}}^2\times {\mathrm{Z}}_{\mathrm{m}\mathrm{n}})$$

(1)

$${\mathrm{Q}}_{\mathrm{l},\mathrm{m}\mathrm{n}}=\mathfrak{I}({\mathrm{I}}_{\mathrm{m}\mathrm{n}}^2\times {\mathrm{Z}}_{\mathrm{m}\mathrm{n}})$$

(2)

$${\mathrm{Z}}_{\mathrm{m}\mathrm{n}}={\mathrm{R}}_{\mathrm{m}\mathrm{n}}+\mathrm{j}{\mathrm{X}}_{\mathrm{m}\mathrm{n}}$$

(3)

where $P_{l,mn}, Q_{l,mn}$ represent the active and reactive loss of the branch connecting buses m and n; $Z_{mn}$ represents the branch impedance and $R_{mn}, X_{mn}$ are its components; $I_{mn}$ represents the branch current passing between the same buses; The symbols $\mathfrak{R},\mathfrak{I}$ refer to the real and imaginary part of a vector.

The power flow solution is based on the forward/backward sweep method (FBSM) [27,28]. The FBSM consists of two sequential steps: forward and backward. In the forward step, the branch currents are calculated as (refer to Figure 1):

$$I_{dn}=conj\left({\displaystyle \frac{P_{dn}+j{Q}_{dn}}{V_n}}\right)$$

(4)

$$I_{mn}=I_{dn}+\sum _r{I}_{nr}+I_{EVCS}-I_{PV}-I_{DSC}$$

(5)

In the backward step, the node voltages are calculated as:

$$V_n=V_m-I_{mn}{Z}_{mn}$$

(6)

These steps are repeated until the difference between the voltage values at the current and previous iterations reaches a predetermined accuracy.

If the PV units supply real power to the bus $n$ with a magnitude of $P_{PV}$, the DSC supplies reactive power to the same bus by an amount of $Q_{DSC}$, and an EVCS is connected to the same bus, the power balance equations are as follows.

$$P_n=P_m+P_{PV}-P_{dn}-{P_{EVCS}-P}_{l,mn}$$

(7)

$$Q_n=Q_m\pm Q_{DSC}-Q_{dn}-Q_{l,mn}$$

(8)

The $Q_{DSC}$ can be positive or negative, depending on the mode of operation of DSTATCOM, whether it is supplying or absorbing reactive power from the system. For a day simulation, the system demand in terms of active and reactive power is assumed to follow the profiles [29], as shown in Figure 2.

The per-unit demand of a system, as indicated by P_d and Q_d representing active and reactive power, respectively, provides a standardized perspective on power consumption concerning a reference value. The powers follow a similar trend, with a stable, low level from 1:00 to 6:00 a.m., then increasing after that until 9:00 a.m. They remain constant until 5:00 pm, then peak at 6:00 p.m. After 6:00 p.m., the demands subsequently declined until the end of the day.

2.2. Modeling of Photovoltaics

In the domain of photovoltaic output power calculation, researchers and authors have employed various approaches to assess the efficiency and performance of solar modules. Certain professionals have thoroughly examined the complex aspects of circuit models [30], evaluated the electrical properties and behavior of the system to determine precise power outputs. Conversely, an alternative perspective has adopted probabilistic models [15], integrating statistical techniques to address uncertainties and fluctuations in solar irradiance and environmental factors. Moreover, others have chosen a more direct method, employing predefined curves [13,29], which illustrate the per-unit output power or irradiation of the module under particular operating conditions. These varied methodologies underscore the intricacy and adaptability inherent in assessing solar power-producing systems. It is well known that the output power of a PV cell depends on solar irradiation and temperature in a probabilistic manner. Hence, for each hour, the PV output power is calculated as [15,31]:

$$P_{PV}\left(t\right)=\alpha \left(t\right)\times I_{sc}\left(t\right)\times V_{oc}\left(t\right)$$

(9)

$$I_{sc}\left(t\right)={\displaystyle \frac{s}{1000}}\left[I_{sc,STC}+k_i\left(T_c\left(t\right)-25\right)\right]$$

(10)

$$V_{oc}\left(t\right)=V_{oc,STC}+k_v\left(T_c\left(t\right)-25\right)$$

(11)

$$\alpha \left(t\right)={\alpha }_o\left(t\right)\times \left[1-r_s\left(t\right)\right]$$

(12)

$${\alpha }_o(t)={\displaystyle \frac{V_{\beta }\left(t\right)-\ln \left[V_{\beta }\left(t\right)+0.72\right]}{V_{\beta }\left(t\right)+1}}$$

(13)

$$V_{\beta }\left(t\right)=V_{oc}\left(t\right)\times {\displaystyle \frac{q}{nk\times \left[T_c\left(t\right)+273.5\right]}}$$

(14)

$$r_s\left(t\right)=R_s\times {\displaystyle \frac{I_{sc}\left(t\right)}{V_{oc}\left(t\right)}}$$

(15)

$$T_c\left(t\right)=T_a\left(t\right)+s\times {\displaystyle \frac{N_{OCT}-20}{0.8}}$$

(16)

The solar irradiance uncertainty is obtained using the beta probabilistic distribution function (pdf) as follows:

$$pdf\left(s\right)=\left\{\begin{array}{l}{\displaystyle \frac{\Gamma \left(\omega +\psi \right)}{\Gamma \left(\mathsf{\omega }\right)\times \Gamma \left(\mathsf{\psi }\right)}}\times s^{\omega -1}\times {\left(1-s\right)}^{\omega -1} for 0\le s\le 1, \omega \ge 0, \psi \ge 0\\ 0 otherwise\end{array}\right.$$

(17)

$$\omega =\mu \left[{\displaystyle \frac{\mu \left(\mu +1\right)}{{\sigma }^2}}-1\right]$$

(18)

$$\psi =\left(1-\mu \right)\left[{\displaystyle \frac{\mu \left(\mu +1\right)}{{\sigma }^2}}-1\right]$$

(19)

By applying the previous modeling equations for the PV modules, a normalized power curve is obtained, as shown in Figure 3.

2.3. Modeling of DSTATCOM

The DSTATCOM is a device that typically consists of a DC/AC converter, a coupling transformer, and a DC source, and is connected at a specific point in the distribution system. DSTATCOM operates by injecting reactive power into the system to regulate voltage levels and improve power factor [32,33]. By dynamically controlling the flow of reactive power, a DSTATCOM helps stabilize the grid, reduce losses, and improve the overall efficiency of the power distribution system. The reactive power supplied by DSTATCOM is calculated as [26]:

$$Q_{DSC}={\displaystyle \frac{V_n.{(V_n-V}_{sh})}{X_{ct}}}$$

(20)

2.4. Modeling of EVCS

The EVs consist of batteries that can be charged from the utility (G2V mode) or discharged (V2G mode), depending on the control method used. In this work, G2V is only considered. In the G2V mode, the EVs are extra loads to the system. To prevent voltage deregulation in the distribution system, the charging level and charging rate must be controlled. The power of the EV’s battery is given as [34]:

$$P_{EV}(t)={\displaystyle \frac{E_{ev}\left(t\right)-E_{ev}\left(t-\Delta t\right)}{\Delta t}}$$

(21)

The state-of-charge (soc) of any battery can be calculated as [12]:

$$soc\left(t\right)=soc\left(t-\Delta t\right)+{\eta }_c{\displaystyle \frac{P_{EV}\left(t\right)}{C_B}}$$

(22)

$$soc\left(t\right)=soc\left(t-\Delta t\right)-{\displaystyle \frac{P_{EV}\left(t\right)}{C_B\times {\eta }_d}}$$

(23)

The total power of the EVCS is the sum of all powers of EV individuals:

$$P_{EVCS}\left(t\right)=\sum _{i=1}^{n_{EV}}{P}_{EV,i}\left(t\right)$$

(24)

In this study, the total load of ECVS is assumed to follow the profile [29], as shown in Figure 4.

Initially, the power starts at around 0.77 pu, dips slightly, and then steadily rises to a peak of 1.0 pu at approximately 12 h. Subsequently, the power gradually decreases, reaching approximately 0.78 pu by the end of 24 h.

3. Problem Formulation

This section outlines the mathematical formulations of the objective functions used in this study, along with the problem and system constraints. Three objective functions are implemented in the study to minimize system power loss, maximize the number of PV units, and maximize the number of EVs in the EVCS. The SFOA optimizes the sites and sizes of the DTSTATCOM devices, the EVs per station, and the PV units.

3.1. Objective Functions

The power losses of any branch of the distribution system are calculated from the branch current and its impedance as:

$$P_{TL}=3\times \sum _{i=1}^{Nb}{I}_b^2\times R_b$$

(25)

$$Q_{TL}=3\times \sum _{i=1}^{Nb}{I}_b^2\times X_b$$

(26)

The first objective function, $f_{O1}$, is as follows:

$$f_{O1}=\mathrm{m}\mathrm{i}\mathrm{n}\left(P_{TL}\right)$$

(27)

If the total power of the EVs per station is P_EVCS, the second objective function $f_{O2}$ is calculated as:

$$f_{O2}=\mathrm{m}\mathrm{a}\mathrm{x}\left(P_{EVCS}\right)$$

(28)

The third objective function $f_{O3}$, aims to increase the power of the PV units as:

$$f_{O3}=\mathrm{m}\mathrm{a}\mathrm{x}\left(P_{PV}\right)$$

(29)

Here, we are dealing with multiple objectives in optimization problems with conflicting objectives (one to be minimized and two to be maximized), and multi-objective optimization (MOO) is employed using a weighted sum method. The overall objective function is expressed as:

$$f_{OT}=k_1\times f_{O1}-\left(k_2\times f_{O2}+k_3\times f_{O3}\right)$$

(30)

$$k_1+k_2+k_3=1.0$$

(31)

It is worth noting the negative sign for both the second and last objective functions to ensure they are minimized. The power for both PVs and EVs is calculated based on their optimized numbers. Then, the powers are calculated by multiplying these numbers by the rated power of each. The rated power for the EVs and PVs is 22 kW and 20 kW [29], respectively. Furthermore, to implement the optimization problem, the three optimization objective functions are normalized by dividing each value by its maximum permissible limit. Thus, the three coefficients (k₁–k₃) exhibit reasonable and comparable values for objectives of equal significance.

3.2. Applied Constraints

The SFOA optimizes the reactive power of the DSTATCOM, the number of EVs per station, and the power capacity of the PV units while maintaining three constraints within predetermined levels. These constraints are summarized as follows.

During the day, the voltage at any bus should satisfy the following limits for the minimum and maximum voltage.

$$V_{L, min}\le V_i\le V_{L,max}$$

(32)

Any branch current inside the system shouldn’t exceed its allowable limit.

$$I_b\le I_{L,max}$$

(33)

The number of EVs inside the EVCS is limited by the area provided and the allowable total demand of the station.

$${n_{EV,min}\le n}_{EV}\le n_{EV,max}$$

(34)

At any location, the number of PV units is restricted to the allowable limits.

$${n_{PV,min}\le n}_{PV}\le n_{PV,max}$$

(35)

The reactive power generated by the DSTATCOM is bound to its allowable limits.

$${Q_{DSC,min}\le Q}_{DSC}\le Q_{DSC,max}$$

(36)

The load flow constraints are also applied as listed in Equations (7) and (8).

3.3. Starfish Optimization Algorithm (SFOA)

The SFOA is a bio-inspired metaheuristic optimization algorithm that first appeared in 2025 [35]. Like any optimization algorithm, it has three main phases: initialization, exploration, and exploitation. The position of any starfish in the initialization phase is expressed as:

$$X_{ij}=l_j+r\left(u_j-l_j\right), i=1:N, j=1:D$$

(37)

where $X_{ij}$ represents the jth position of the ith starfish; r is a random number (0,1); $u_j$ and $l_j$ are the upper and lower bounds; N is the population size, and D is the dimension of variables.

In the exploration phase, the positions of the starfish are updated as:

$$Y_{i,p}=X_{i,p}+a_1\left(X_{best,p}-X_{i,p}\right)\cos \theta , r\le 0.5$$

(38)

$$Y_{i,p}=X_{i,p}-a_1\left(X_{best,p}-X_{i,p}\right)\sin \theta , r>0.5$$

(39)

where $Y_{i,p}$ represents the obtained starfish position while $X_{i,p}$ represents the current position; $X_{best,p}$ is the best position of p-dimension; $a_1$ and $\theta$ are calculated as follows:

$$a_1=\pi \left(2r-1\right)$$

(40)

$$\theta ={\displaystyle \frac{\pi }{2}}\times {\displaystyle \frac{T}{T_{max}}}$$

(41)

where $T$ and $T_{max}$ are the current and maximum iteration.

The boundaries of the designed variables are checked to be within the limits of the problem, as:

$$X_{i,p}=\left\{\begin{array}{l}{Y}_{i,p}, l_{b,p}\le Y_{i,p}\le u_{b,p}\\ X_{i,p}, otherwise\end{array}\right.$$

(42)

where $p$ denotes the updated dimension. If the dimension $D$ is less than 5 ($D\le 5$), the updated positions of starfish are calculated from:

$$Y_{i,q}=E_t{X}_{i,p}+A_1\left(X_{k1,p}-X_{i,p}\right)+A_2\left(X_{k2,p}-X_{i,p}\right)$$

(43)

where $A_1$ and $A_2$ are random numbers (−1,1); $X_{k1,p}$ and $X_{k2,p}$ are two random positions of a p-dimensional starfish; $E_t$ is calculated as follows:

$$E_t={\displaystyle \frac{T_{max}-T}{T_{max}}} \cos \theta$$

(44)

In the exploitation phase, the distances between the best position and starfish positions are calculated as:

$$d_m=\left(X_{best}-X_{mp}\right), m=1:5$$

(45)

where $d_m$ represents the five distances obtained between the starfish and the best position; $mp$ represents a random five-starfish. The updated position of the starfish is as:

$$Y_i=X_i+r_1{d}_{m1}+r_2{d}_{m2}$$

(46)

where $r_1$ and $r_2$ represent random numbers and $d_{m1}$ and $d_{m2}$ are also random numbers from $d_m$.

When other predators partially eat the starfish, it takes time to regenerate its organs. This situation is simulated with a slow speed of position as:

$$Y_i=X_i \mathrm{e}\mathrm{x}\mathrm{p}\left({\displaystyle \frac{-N\times T}{T_{max}}}\right)$$

(47)

As before, the new positions are checked to ensure they are within the accepted boundaries.

4. Simulation Results

4.1. Statistical Comparison of SFOA with Benchmarks

The performance of the Starfish Optimization Algorithm (SFOA) was benchmarked, as listed in

Table 1. Performance of SFOA and other algorithms for power loss minimization in the 33-bus system.

Algorithm	Minimum	Average	Worst	Median	Std	% Reduction
SFOA	72.784	72.824	73.671	72.784	0.169	--
FPA	74.014	76.953	80.242	76.925	1.522	5.37%
HHO	73.042	79.807	89.988	79.257	3.921	8.76%
MVO	72.784	73.655	78.452	72.784	1.982	1.13%
SMA	72.784	74.184	78.452	72.784	2.363	1.83%
SSA	72.784	74.081	86.855	72.784	3.704	1.69%
PSO	72.784	73.125	77.891	72.784	1.296	3.06%

, against six established metaheuristic algorithms—Flower Pollination Algorithm (FPA), Harris Hawks Optimization (HHO), Multi-Verse Optimizer (MVO), Slime Mould Algorithm (SMA), Salp Swarm Algorithm (SSA), and Particle Swarm Optimization (PSO)—for the allocation of three distributed generators in the IEEE 33-bus distribution system. All algorithms were executed under identical conditions of 100 particles, 100 iterations, and consistent system constraints, ensuring a fair comparison. SFOA achieved the lowest average power loss (72.824 kW), outperforming all other methods. The relative reductions in average loss were most pronounced against HHO (8.76%) and FPA (5.37%), highlighting SFOA’s superior convergence in complex search spaces. Even against widely used PSO, SFOA achieved a 3.06% reduction, confirming its advantage over conventional approaches.

In terms of worst-case performance, SFOA demonstrated remarkable robustness, with a maximum loss of 73.671 kW. This value was substantially lower than those of HHO (89.107 kW) and SSA (86.855 kW), which exhibited significant variability and susceptibility to poor-quality solutions. The standard deviation of SFOA (0.169) was also the lowest among all algorithms, indicating highly consistent performance across multiple runs. By contrast, SSA and HHO recorded deviations of 4.500 and 3.921, respectively, reflecting unstable behavior. The median values further reinforce SFOA’s reliability, as it matched the minimum loss, demonstrating its ability to reach near-optimal solutions consistently. While other algorithms occasionally achieved similar minimum losses (72.784 kW), their higher averages and worst-case values underscore the superior stability of SFOA.

Moreover, the SFOA is compared with the same algorithms listed in

Table 2. Performance of the SFOA and other algorithms for power loss minimization in the 69-bus system.

Algorithm	Minimum	Average	Worst	Median	Std	% Reduction
SFOA	69.395	69.398	69.417	69.395	0.007	--
FPA	70.585	72.179	73.421	72.253	0.726	3.86%
HHO	69.924	73.999	80.488	72.677	3.19	6.23%
MVO	69.395	70.124	73.052	69.539	1.176	1.04%
SMA	69.395	69.739	71.611	69.528	0.656	0.49%
SSA	69.395	71.15	78.041	70.144	2.056	2.47%
PSO	69.395	70.644	74.457	70.127	1.446	1.77%

by simulating the 69-bus system to optimize the allocation of three DGs to reduce system losses. The SFOA achieved the lowest average power loss of 69.396 kW, outperforming all other algorithms. The percentage reductions in average loss compared to the benchmarks were as follows: 3.86% over FPA (72.179 kW), 6.23% over HHO (74.009 kW), 1.04% over MVO (70.124 kW), 0.49% over SMA (69.739 kW), 2.47% over SSA (71.150 kW), and 1.77% over PSO (70.644 kW). These reductions underscore the SFOA’s superior convergence behavior and its ability to identify high-quality solutions consistently.

In terms of worst-case performance, SFOA recorded a maximum loss of 69.417 kW, significantly lower than the worst outcomes of HHO (80.488 kW), SSA (78.041 kW), and PSO (74.457 kW). This indicates enhanced robustness and reliability, as SFOA consistently avoids poor-quality solutions across multiple runs. The standard deviation of SFOA (0.007) was the lowest among all algorithms, demonstrating exceptional consistency and minimal variability. In contrast, HHO and SSA exhibited high standard deviations of 3.19 and 2.056, respectively, reflecting unstable performance and sensitivity to initial conditions. Furthermore, the median SFOA value (69.395 kW) matched its minimum, further reinforcing its ability to reach near-optimal solutions consistently. While other algorithms, such as MVO, SMA, SSA, and PSO, also achieved the same minimum value, their higher average and worst-case losses highlight the superior reliability and repeatability of SFOA. Compared to benchmark algorithms, the Starfish Optimization Algorithm (SFOA) consistently achieved lower average power losses, with reductions of 6.23% over HHO, 3.86% over FPA, 2.47% over SSA, 1.77% over PSO, 1.04% over MVO, and 0.49% over SMA. These results confirm SFOA’s superior efficiency, reliability, and convergence stability under identical optimization conditions.

4.2. Locating EVCS, DSTATCOM, and PV Devices

The proposed methodology for integrating EVCSs with PV units and DSTATCOM devices is tested on the modified 51-bus distribution system shown in Figure 5. The system voltage is 11 kV, with a total demand of 2463 kW and 1569 kVar [36]. The following case studies are analyzed and presented in this work.

In the first stage of the EVCS planning, the best locations inside the distribution system are identified and optimized. Thus, the locations of the EVCSs, DSTATCOM, and PV units are determined using the SFOA optimization algorithm. Once these devices are located, they will be fixed through the study. Three locations are considered for each DSTATCOM and PV device. On the other hand, three scenarios are considered: a single charging station, two charging stations, and three charging stations. In this case, the objective is to decrease the power loss of the system, as it is essential for optimal operation. The EVCS demand is chosen to be 616.25 kW (25% of the system demand) for a single EVCS. The PV and DSTATCOM are simulated at a particular time of the day. The system performance, including losses and minimum voltage at optimal device sites, is listed in

Table 3. Planning of EVCSs with DSTATCOM and PV devices.

Devices Parameters	1 EVCS		2 EVCSs		3 EVCSs
	Bus No.	Size (kW)	Bus No.	Size (kW)	Bus No.	Size (kW)
EVCS	4	616.25	44, 2	616.25, 616.25	47, 2, 41	616.25, 616.25, 616.25
PV	4, 43, 10	1787.10, 320.42, 808.44	46, 44, 4	732.51, 901.22, 1542.81	47, 4, 44	1889.91, 1689.10, 287.67
DSTATCOM	6, 49, 14	864.17, 199.08, 232.3	6, 46, 43	722.24, 435.03, 149.73	15, 48, 6	207.46, 246.66, 785.48
System loss (kW)	26.62		29.69		30.5
Reactive loss (kVar)	11.169		13.525		14.404
TVD	0.5045		0.52138		0.5584
Minimum voltage, Vmin (pu)	0.9786		0.9758		0.9763

for the three cases.

The integration of electric vehicle charging stations (EVCSs) into a distribution network presents a complex planning challenge, necessitating the co-optimization of compensatory devices to maintain system stability. This analysis evaluates the system’s performance under three distinct penetration levels of EVCSs, each scenario supported by the optimal placement and sizing of three photovoltaic (PV) units and three DSTATCOM devices. The key performance indicators—system active power loss, reactive power loss, total voltage deviation (TVD), and minimum voltage—have been assessed for each case.

A clear trend is observed where an increasing number of EVCSs leads to a degradation of system performance, even with optimal compensation. In the scenario with a single EVCS at bus 4 with a size of 616.25 kW, the system performance was most favorable. The PV systems, located at buses 4, 43, and 10 with a combined capacity of 2915.94 kW, and DSTATCOMs at buses 6, 49, and 14 providing 1295.55 kVar of support, resulted in the lowest recorded system losses (26.62 kW active, 11.169 kVar reactive), the lowest TVD of 0.5045 pu, and the highest minimum voltage of 0.9786 pu.

The introduction of a second EVCS at bus 2, which doubles the total EV load to 1232.5 kW, resulted in a measurable decline across all indices, despite strategic device placement. The PV units at buses 46, 44, and 4 totaled 3176.51 kW, and the DSTATCOMs at buses 6, 46, and 43 provided 1307 kVar of support. Consequently, system losses increased to 29.69 kW and 13.525 kVar, representing an increase of 11.5% and 21.1%, respectively. The TVD worsened to 0.52138 pu, and the minimum voltage declined to 0.9758 pu, indicating a less flat and more stressed voltage profile.

The system with three EVCSs, located at buses 47, 2, and 41 for a total load of 1848.75 kW, exhibited the most stressed operation. Although the optimization strategy deployed the largest aggregate PV capacity (3866.67 kW at buses 47, 4, and 44) to counteract the load, the system’s performance was the poorest among the cases. The DSTATCOMs at buses 15, 48, and 6 provided 1239.6 kVar of support. The active and reactive power losses increased to 30.5 kW and 14.404 kVar, representing 14.6% and 29.0% rises from the base single-EVCS case. The TVD increased significantly to 0.5584 pu, and the minimum voltage remained depressed at 0.9763 pu.

The analysis demonstrates that while the coordinated placement of PV generation and DSTATCOM reactive power support is effective in mitigating the negative impacts of EVCS load, its ability to compensate fully is finite. The consistent upward trend in system losses and voltage deviation with each additional EVCS underscores the escalating stress on the network infrastructure. This finding highlights a critical consideration for system planners: beyond a certain level of EV penetration, distributed compensation alone may be insufficient, potentially necessitating more extensive network reinforcement to ensure reliable and efficient operation.

4.3. System Performance During 24 h

The modified 51-bus system is simulated for 24 h with a one-hour time step to analyze system performance under stochastic demand, renewable energy sources, and EVCS daily profiles. The optimal locations, as listed in Table 1, are maintained for EVCSs, PV units, and DSTATCOM devices. The three case studies—single EVCS (Case 1), two EVCSs (Case 2), and three EVCSs (Case 3)—are simulated, analyzed, and compared. For each case, the SFOA optimizes the sizes of the DSTATCOM units (DCS₁, DCS₂, and DCS₃) to minimize system losses. Additionally, the numbers of PV units and vehicles per station are optimized to ensure system and voltage constraints are met. The sizes of PV and EVCS considered are 20 kW and 22 kW [29], respectively. Accordingly, the number of EVs and PV units for each case is initially calculated from Table 1 and then optimized to prevent constraint violations, particularly those related to voltage limits.

The boxplot of Figure 6 shows the distribution of minimum voltage levels, given in per unit (pu), across three different scenarios involving the integration of electric vehicle charging stations (EVCSs) into the distribution system. In Case 1, with one EVCS added, the interquartile range is approximately from 0.948 pu to 0.972 pu, with a median around 0.962 pu, reflecting a stable voltage profile with slight variation and some outliers slightly beyond this range. Case 2, with two EVCSs, has a broader spread, with the interquartile range from about 0.92 pu to 0.969 pu and a lower median near 0.93 pu, indicating more voltage fluctuation and sags, as shown by the extended lower whisker close to 0.90 pu. In contrast, Case 3, with three EVCSs, displays a more concentrated distribution, with the interquartile range between 0.92 pu and 0.955 pu and a median close to 0.93 pu, suggesting better voltage regulation than Case 2 but slightly more variation than Case 1. Overall, the plot shows a gradual decrease in minimum voltage stability from Case 1 to Case 2 due to the higher EVCS load, with a partial recovery in Case 3, possibly because of improved system compensation from the DSTATCOM devices.

The maximum voltage variations during the day for the three case studies involving the integration of EVCSs into the distribution system are shown in the boxplot of Figure 7. In Case 1, with a single EVCS, the maximum voltage remains tightly clustered around 1.00 pu, with minimal variation and no significant outliers, indicating a stable voltage profile under this setup. Case 2, which includes two EVCSs, shows a slight increase in maximum voltage, reaching up to approximately 1.02 pu with a median close to 1.00 pu, suggesting a modest rise in voltage due to increased reactive power from the three DSTATCOM devices. Case 3, with three EVCSs, exhibits the most notable increase, characterized by a larger interquartile range and outliers extending to just below 1.04 pu, indicating greater voltage fluctuations resulting from cumulative reactive power effects. This progressive increase in maximum voltage from Case 1 to Case 3 highlights the influence of the additional active power injected by the three PV units and the reactive power from the three DSTATCOM devices.

A significant index for the voltage of the distribution system is the TVD. In this case, the TVD is calculated for every hour of the day and is shown in Figure 8 as a boxplot to illustrate its variability throughout the day. The TVD is recorded across the three case studies incorporating EVCSs, PV units, and DSTATCOM devices. The TVD quantifies cumulative bus voltage deviations from the nominal 1.0 pu value, with lower figures indicating superior voltage stability. In Case 1, involving a single EVCS integration, the median TVD is approximately 1.2 pu, with an IQR from 0.8 to 1.4 pu and whiskers extending from 0.25 to 1.8 pu, reflecting minimal variability and stable performance under light load. Case 2, with two EVCSs, shows an elevated median of 1.35 pu, with wider IQR and whiskers, indicating increased voltage stress due to additional charging demand. In Case 3, where three EVCSs are integrated, the median reaches 1.85 pu, with higher IQR and whisker values than in Case 2, indicating the highest deviations due to the increased demand from three EVCSs, particularly in the evening when power from the PV units is unavailable.

The corresponding power loss of the system for the three case studies over 24 h, incorporating one, two, and three electric vehicle charging stations (EVCSs), respectively, alongside three photovoltaic (PV) units and three Distribution Static Compensator (DSTATCOM) devices, is shown in Figure 9. In Case 1 (single EVCS), power loss remains relatively low, fluctuating between approximately 20 and less than 100 kW, with a gradual decline from early hours (1–6 h), due to lower demands of the EVCS and system demand. During the second third (6–18 h) of the day, when PVs are activated during daylight hours and DSTATCOM support, the system loss is notably decreased due to the presence of PV power. In the last third of the day (18–24 h), the system losses occur due to two reasons: the absence of PV power and an increase in system demand.

Case 2 (two EVCSs) shows a moderate increase, with power loss ranging from 20 to over 150 kW around 21 h, indicating a higher load demand that slightly exceeds the compensatory effects of PV and DSTATCOM, especially during peak charging times of EVCSs. Following the same pattern, Case 3 (three EVCSs) shows the highest power loss, reaching up to 250 kW around 21 h, with a broader range of 50 to 250 kW throughout the day. This indicates significant strain on the system due to increased EV charging, despite the presence of PV units and DSTATCOM devices, which appear insufficient to fully offset the increased demand during peak hours. Overall, the results reveal a clear trend of rising power loss with the addition of EVCSs, emphasizing the need for better coordination or expanding the capacity of DER to maintain efficiency, especially during high-demand periods.

The reactive power loss of the system follows the same pattern as the previous power loss, as shown in Figure 10. The findings reveal a progressive increase in reactive power losses with the addition of EVCSs, with Case 3 demonstrating the highest losses (190 kVar), especially during the last third of the day after the PV units are unavailable. Throughout all cases, the presence of three PV units and three DSTATCOM devices helps to manage reactive power within the system. Nevertheless, the results suggest that the DSTATCOMs might struggle to fully offset the augmented reactive power demand resulting from multiple EVCS integrations, especially during peak demand periods.

On the other hand, the incorporation of supplementary EVCSs is correlated with a progressive increase in the system’s perceived power demand throughout the day, as shown in Figure 11. Case 1 displays the minimal apparent power, peaking at roughly 950 kVA, whilst Case 3 reveals the maximum demand, attaining nearly 1350 kVA during peak periods. This graph shows that the presence of EVCSs significantly increases the system’s load, especially at night when charging activity is expected to increase due to PV power shortages. Conversely, the system experiences a significant decrease in perceived power around midday, attributed to increased PV generation, thereby reducing dependence on the utility power source.

The optimal photovoltaic power for each case study is illustrated in Figure 12. In Case 1, the output of the three photovoltaic units is relatively consistent, reaching roughly 1780, 800, and 320 kW for PV1, PV2, and PV3, respectively, around midday. The maximum power output of photovoltaic systems is 2900 kW. The presence of a single EVCS does not impose a significant additional load on the system, enabling the PV units to operate effectively while supplying power to both the grid and the EVCS. This scenario demonstrates the successful integration of renewable energy sources with minimal impact on overall system stability. The integration of two EVCSs in the second scenario increases system demand, as evidenced by the operational dynamics of the PV units. Despite the overall photovoltaic power production peaking at around 1540, 900, and 740 kW for PV1, PV2, and PV3, respectively, the introduction of the supplementary load increases the power generated by each unit, culminating in a total maximum generated power of 3180 kW. The output during peak sun hours is marginally influenced by the concurrent charging requirements of the two EVCSs, which may directly extract power from the PV units. This interaction highlights the need to balance generation and demand, as the system must manage the increased load while optimizing solar energy use. In Case 3, the connection of three EVCSs to the system is anticipated to enhance the PV power production. The maximum output is approximately 1700, 300, and 1900 kW for PV1, PV2, and PV3, respectively, totaling 3900 kW, indicative of heightened demand and competition for solar energy resources. The concurrent operation of numerous EVCSs results in a significant increase in charging power, necessitating system stabilization via DSTATCOMs. Notwithstanding the elevated demand, the PV units continue to perform admirably, demonstrating the system’s tolerance to increased loads.

The SFOA optimizes DSTATCOM devices to reduce overall system losses throughout the day while incorporating EVCSs and PV units. The optimum values of the DSTATCOM devices for each case study are presented in Figure 13. The designations DSC₁, DSC₂, and DSC₃ pertain to the device numbers of the DSTATCOMs. The DSTATCOMs predominantly function in a compensatory manner, delivering reactive power assistance to maintain voltage levels in the presence of a solitary EVCS. In Case 1, the reactive power production from DSC₂ and DSC₃ exhibits minor fluctuations throughout the day, whereas DSC₃ undergoes significant alterations in response to demand changes. The DSC₃ decreases at the onset of the day until the photovoltaic power activates, after which it remains stable during daylight hours. The absence of photovoltaic power at the evening necessitates an increase in reactive power to stabilize voltage and minimize system losses. The highest corrected powers of the DSTCOM devices are 442 kVar for DSC₁, 100 kVar for DSC₂, and 88 kVar for DSC₃, around 7 pm. The highest compensated power is 630 kVar. The oscillations indicate the efficiency of DSTATCOMs in adapting to changes in system demand, hence facilitating the integration of the single EVCS with the current PV generation.

In Case 2, the addition of a second EVCS leads to a more dynamic reactive power profile, particularly for DSC₃. The maximum injected reactive powers are 450 kVar for DSC₁, 74 kVar for DSC₂, and 193 kVar for DSC₃, respectively. The reactive power requirements escalate (peak power is 717 kVar) as the two EVCSs draw additional current, requiring the DSTATCOMs to respond more vigorously to maintain voltage stability. The DSTATCOMs exhibit reactive power outputs that occasionally take negative values, indicating their ability to provide reactive power to offset increased demand. In Case 3, the incorporation of a third EVCS significantly complicates the system’s reactive power dynamics. The DSTATCOMs exhibit greater fluctuations in reactive power output, with notable negative values recorded during peak charging intervals. This indicates a substantial need for reactive power adjustment as the system struggles to handle the increased load from all three EVCSs. The highest compensated reactive powers are 631, 89, and 115 kVar for DSC₁, DSC₂, and DSC₃, respectively, yielding a total maximum power of 835 kVar. DSTATCOMs actively provide reactive power, underscoring their essential role in maintaining voltage stability and power quality as demand increases.

The power profiles of EVCSs across three case studies demonstrate the effect of increasing the number of charging stations on overall power consumption and system efficiency, as illustrated in Figure 14. In Case 1, with a single EVCS, demand remains constant, reaching a peak of approximately 616 kW at noon, facilitating efficient resource management without jeopardizing system stability. In Case 2, adding a second EVCS increases average power production to approximately 968 kW at noon, leading to greater variations and necessitating a proactive system response to manage the increased load. Case 3, with three EVCSs, experiences the highest demand, reaching approximately 1848 kW at noon, posing significant challenges for system management, particularly in maintaining voltage stability and preventing overloads. The cumulative demand of the EVCSs peaks at 3432 kW at noon.

4.4. Comparison of the System Performance During the Different Case Studies

A comparison of the three case studies is presented to clarify the effects of increasing EVCSs on the distribution system and the related parameter values, as shown in

Table 4. System performance in the three case studies.

Parameter	Case 1	Case 2	Case 3
Total active energy loss (kWh)	980.53	1589.37	2779.12
Total reactive energy loss (kVarh)	814.57	1099.92	1991.02
DSTATCOM reactive power (MVar)	11.019	12.018	13.742
Supplied utility energy (MVA)	12.800	13.854	18.248
PV supplied energy (MWh)	21.728	23.826	29.221
EVCS energy (MWh)	12.411	19.503	37.233
Maximum voltage (pu)	1.0058	1.0207	1.0370
Minimum voltage (pu)	0.9355	0.9002	0.9003
Average TVD (pu)	1.083	1.255	1.679
Maximum utility current (A)	148.54	167.82	212.99

. The total active energy loss exhibits a distinct upward trend as the number of EVCSs increases within the system. The increase is significant, with a 62.1% escalation in active energy loss from Case 1 to Case 2 and an additional 74.9% jump from Case 2 to Case 3. This trajectory highlights a clear correlation between the expansion of EVCSs and the escalation of active energy losses, demonstrating a significant impact on the system’s overall energy efficiency. Correspondingly, the total reactive energy loss consistently increases across the three scenarios, with Case 3 exhibiting an 81% increase relative to Case 2. The increment from Case 1 to Case 2 is 35%. This graph highlights the increasing reactive energy requirements within the system as the number of EVCSs increases. The DSTATCOM’s reactive power production responds favorably to the escalating demands driven by the growing number of EVCSs. The documented 14.4% augmentation in reactive power production from Case 2 to Case 3, together with a 9.1% escalation from Case 1 to Case 2, exemplifies this tendency. The SFOA regulates these increases to mitigate excess demand and system losses by incorporating additional EVCSs. Moreover, the utility energy supplied shows a consistent increase across cases, with Case 3 witnessing a notable 31.7% increase in energy delivered relative to Case 2. In Case 2, the utility increases its output by 8.23% in response to the additional demand from the second EVCS. This augmentation signifies the system’s enhanced capacity to accommodate escalating energy requirements.

The contribution of photovoltaic units to the system’s energy dynamics shows a steady upward trend, with Case 3 exhibiting a significant 22.6% increase in PV-supplied energy relative to Case 2. Furthermore, there is an approximate increase in the percentage from Case 1 to Case 2. This progression highlights the SFOA’s ability to determine the optimal quantity of PV units required in each instance to meet demand escalations. The energy consumption of EVCS increases markedly as more stations are added. Energy consumption escalates by 57.1% from Case 1 to Case 2, and then by a significant 90.9% surge from Case 2 to Case 3. The maximum voltage values exhibit a consistent rise across the cases. Case 2 shows a 1.5% increase compared to Case 1, whereas Case 3 demonstrates an additional 1.6% rise in relation to Case 2. Although these increments are minimal, they are crucial for voltage stability, ensuring that the peak voltage in the scenarios remains beneath the permissible threshold of 1.05 pu, as mandated by the SFOA. Simultaneously, the minimum voltage diminishes in each instance; yet, the 0.9 pu threshold remains satisfied throughout all scenarios. The decrease in minimum voltage directly affects the TVD, which escalates as system demand intensifies and voltage levels decrease. Notwithstanding this, the average TVD remains satisfactory for medium-sized systems, such as the 51-bus system. The maximum utility current consistently increases with the number of EVCSs installed. Case 2 exhibits a 13% augmentation in maximum utility current in comparison to Case 1, although Case 3 reveals a substantial 26.9% increase relative to Case 2.

5. Conclusions

This study explored the optimization of distribution systems that incorporate Photovoltaic (PV) units, Electric Vehicle Charging Stations (EVCSs), and DSTATCOM devices using the Starfish Optimization Algorithm (SFOA). Through the SFOA’s multi-objective optimization approach, this research successfully identified the best sites and sizes for PV units, EV charging stations, and DSTATCOM reactive power to achieve goals such as minimizing system losses, increasing PV capacity, and improving EVCS power. The analysis and comparison of case studies with varying numbers of EVCSs in a 51-bus distribution system over 24 h yielded significant results. Notably, this study found that PV hosting energy and EVCS energy increased across the different cases, reaching specific values for each scenario. Additionally, the optimized DSTATCOM reactive powers were calculated for each case study, ensuring that system constraints remained within acceptable limits, including voltage levels, utility current considerations, and power flow equations. These results demonstrate the effectiveness of the SFOA in optimizing distribution systems with PV units, EVCSs, and DSTATCOM devices, emphasizing its ability to improve system efficiency and meet key objectives while maintaining operational constraints. Compared with other optimization algorithms, the SFOA consistently demonstrated superior performance in minimizing distribution system power losses. In the 33-bus system, the SFOA achieved up to an 8.76% reduction in average loss compared to HHO, with notable improvements over the FPA (5.37%) and PSO (3.06%), while also outperforming the SMA, SSA, and MVO by smaller margins. Similarly, in the 69-bus system, the SFOA reduced average losses by 6.23% relative to HHO and 3.86% compared to the FPA and achieved moderate gains over the SSA (2.47%), PSO (1.77%), MVO (1.04%), and SMA (0.49%). These consistent reductions across different network sizes highlight the SFOA’s robustness, efficiency, and reliability under identical optimization conditions, confirming its potential as a powerful tool for distributed generation planning in modern distribution systems.